Ch 3
Use the schematic curve and the z-table to find the proportion of a population less than z = -1.96 and greater than z = +1.96
0.9500
What is the appropriate mathematics to use to find a right body area
1 - An area from the z-table.
What is the appropriate mathematics to use to find a middle body area
1 - a left area from the z-table - a right area from the z-table.
use the schematic curve and the z-table to find the z-score that bounds the top 2.02% of a population
2.05
Intelligent Quotient (IQ) scores are standardized for population to have a mean score of 100 and a standard deviation score of 15. With this knowledge, what percent of the population are eligible to join the Mensa organization (need IQ > 130)?
2.28%
At a local secondary school, the school children were known to run a race with the race times distributed normally with a mean time of 450 seconds and a standard deviation time of 50 seconds. With this information, what is the shortest time and the longest time of the middle 95% of the children
352 seconds, and 548 seconds
Use the schematic curve and the z-table to find what are the z-scores for the first quartile (Q₁), and for the third quartile (Q₃)
(Q₁) is at z = -0.67, and (Q₃) is at z = +0.67 .
In a recent past year, the scores of students taking the ACT college entrance test were found to be distributed normally with a mean score of 18.6 and a standard deviation score of 5.85. What is the probability that a randomly chosen student from this population would have an ACT score lower than 21
0.6591
What is the range of z-scores
-∞ < 𝓏 < +∞
Use the schematic curve and the z-table to find the probability of an individual having a z-score greater than +2.00
0.0228
For a city where the prices of new homes were distributed normally with a mean price of $150,000 and a standard deviation price of $11,000, what proportion of new homes are mid priced (between $125,000 and $139,000)
0.1471
in a recent past year, the scores of students taking the ACT college entrance test were found to be distributed normally with a mean score of 18.6 and a standard deviation score of 5.17. What is the probability that a randomly chosen student from this population would have an ACT score higher than 21.6
0.2810
Use the schematic curve and the z-table to find the probability of an individual in a population following the standard normal curve being less than (or greater than) the mean
0.500
For a city where the prices of new homes were distributed normally with a mean price of $150,000 and a standard deviation price of $1,700, what percentage of home buyers paid more than $152,074
11.12%
The times to complete a mile long race for boys in a local secondary school was known to be normally distributed with a mean time of 460 seconds and a standard deviation time of 60 seconds. With this population, what time separates the fastest 10% of the boys from the other 90%. Note that a faster boy completes the race in less seconds
383.3
At a local secondary school, the school children were known to run a race with the race times distributed normally with a mean time of 450 seconds and a standard deviation time of 50 seconds. With this information, what is the shortest time and the longest time of the middle third (34%) of the children
428 seconds, and 472 seconds
In a factory packaging corn chips, the weight of corn chips put into each bag by a dispensing machine was distributed normally with a mean weight of 48.5 ounces and a standard deviation weight of 0.2 ounces. What weight of corn chips separates the lightest 67% of the bags from the other 33%
48.59 ounces
The times to complete a mile long race for boys in a local secondary school was known to be normally distributed with a mean time of 460 seconds and a standard deviation time of 60 seconds. With this population, what time separates the fastest 90% of the boys from the other 10%. Note that a faster boy completes the race in less seconds
536.8
In a city where the prices of new homes were found to be distributed normally with a mean price of $150,000 and a standard deviation price of $900, what percentage of these new homes cost less than $148,623
6.30%
The tread life of a brand of tire is distributed normally with a mean of 60,000 miles and a standard deviation of 1,000 miles. What mileage separates the longest lasting 4% of these tires (have the highest mileage) from the other 96%
61750
For a city where the prices of new homes were distributed normally with a mean price of $150,000 and a standard deviation price of $1,1,00, what percentage of new homes are mid priced (between $146,500 and $151,500)?
91.24%
What is the appropriate mathematics to use to find a two-tail area
An area from the z-table + an area from the z-table.
What is the appropriate mathematics to use to find a left tail area
An area from the z-table.
Which of the following answers is NOT true of a statistical event.
An event is an area under a normal curve
Why is the distribution of a data set so important
Because the distribution can be used to find the probability of an event
What are the critical parameters of a normal curve
Mean (µ) and standard deviation (σ)
what is the mean (µ) and standard deviation (σ) of the standard normal distribution (z-distribution)
Mean = 0, and standard deviation = 1.
Why is the probability of an event so important in the science of statistics?
Probability of an event can be used to make a better decision.
In the standard normal distribution, what are z-scores used to describe?
The event on the x-axis.
Which of the following answers is NOT true about why the Empirical Rule focuses out to (µ±3σ), but not beyond
The information beyond µ±3σ is much harder to calculate
What is the appropriate mathematics to use to find a right-side area
The larger area from the z-table - the smaller area from the z-table.
What information does an area under the normal curve give?
The probability of an event.
The z-curve is a graph of what distribution
The standard normal distribution.
For a side area in the schematic curve, how many lines are drawn and on which side of the curve are they drawn?
Two lines on the same side.
top blank
area under the curve
On a real number line, a change in the mean shifts a normal curve horizontally, and a change in the standard deviation shifts the normal curve vertically
false
Only one critical parameter is needed to calculate probability with a normal curve.
false
The probability of an event can mean two things: 1. The proportion of the population described by the event. 2. The chance an individual will be randomly selected.
false
There are an infinite number of standard normal distributions
false
x-Values have no units of measurement associated with them.
false
How many normal curves are possible?
infinitely many
A normal curve can be described with one specific mathematical equation, if the values of the variables are known.
true
All normal curves look the same WHEN they are plotted on a graph in terms of their mean +/- their standard deviations.
true
For the Shapiro-Wilk test for normality, a P-value = 0.25 means that the data follow a normal shape
true
Standard deviation (σ) is another way to give the width of a normal curve.
true
The Schematic Curve for z-scores, with a second x-axis in terms of the mean and standard deviation of the x-values, gives the Schematic Curve for x-values.
true
The areas defined in the Empirical Rule of statistics are valid for all normal curves
true
The standard normal distribution ( z-distribution) follows the Empirical Rule of statistics.
true
the area under the standard normal curve = 1.
true
bottom blank
x-value
are the two equations below the same equation with one equation just a reorganization of the other equation? z=x−μ/σ x=μ+z∗σ
yes
middle blank
z-score
